Density conditions with stabilisers for lattice orbits of discrete series representations

2025/05/06 by van Velthoven, Jordy Timo
#FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.03417

Abstract

This note provides elementary proofs for necessary density conditions for frames and Riesz sequences in the lattice orbit of a discrete series representation that involve the projective stabiliser of the vector. The presented approach extends and simplifies known density conditions for Bergman kernels and lattices in semisimple Lie groups.

Citations

• A dynamical approach to sampling and interpolation in unimodular groups
• Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains
• Bergman space zero sets, modular forms, von Neumann algebras and ordered\n groups
• The density theorem for discrete series representations restricted to\n lattices

Related

• The density theorem for discrete series representations restricted to\n lattices
• Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains
• On Kronecker's density theorem, primitive points and orbits of matrices
• On stable lattices and the diagonal group
• Coherent systems over approximate lattices in amenable groups